Certificate for #6256 ⟨a, b, c | aa=1, bbcbcb=1⟩

Completion settings:

• Auxiliary generators:
  1. d = bc
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b

Axiom: aa=1.

Defines rule #1.

Axiom: bbcbcb=1.

Referenced by [4].

Axiom: bc=d.

Defines rule #7.

Referenced by [4], [5], [13].

Overlap of [2] bbcbcb=1 with [3] bc=d:

Critical pair: bdbcb=1.

Reduce LHS:

Referenced by [5], [6], [8], [11], [14].

Overlap of [4] bddb=1 with [3] bc=d:

Critical pair: bddd=c.

Defines rule #3.

Referenced by [7], [8], [9], [10], [12].

Overlap of [4] bddb=1 with [4] bddb=1:

Critical pair: bdd=ddb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8], [9], [14].

Overlap of [5] bddd=c with [6] ddb=bdd:

Critical pair: bdbdd=cb.

Defines rule #10.

Referenced by [11], [12].

Overlap of [5] bddd=c with [6] ddb=bdd:

Critical pair: bddbdd=cdb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [10].

Overlap of [6] ddb=bdd with [5] bddd=c:

Critical pair: ddc=bddddd.

Reduce RHS:

Defines rule #2.

Overlap of [8] cdb=dd with [5] bddd=c:

Critical pair: cdc=ddddd.

Defines rule #5.

Overlap of [7] bdbdd=cb with [4] bddb=1:

Critical pair: bd=cbb.

Flip LHS and RHS.

Defines rule #12.

Referenced by [13].

Overlap of [7] bdbdd=cb with [5] bddd=c:

Critical pair: bdc=cbd.

Defines rule #8.

Overlap of [3] bc=d with [11] cbb=bd:

Critical pair: bbd=dbb.

Flip LHS and RHS.

Defines rule #11.

Overlap of [4] bddb=1 with [6] ddb=bdd:

Critical pair: bbdd=1.

Defines rule #9.